Fluid mechanics Assignment Help




Fluid mechanics is the study of fluids and the forces on them. (Fluids include liquids, gases, and plasmas.) Fluid mechanics can be divided into fluid kinematics, the study of fluid motion, and fluid dynamics, the study of the effect of forces on fluid motion, which can further be divided into fluid statics, the study of fluids at rest, and fluid kinetics, the study of fluids in motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms, that is, it models matter from a macroscopic viewpoint rather than from a microscopic viewpoint. Fluid mechanics, especially fluid dynamics, is an active field of research with many unsolved or partly solved problems. Fluid mechanics can be mathematically complex. Sometimes it can best be solved by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach to solving fluid mechanics problems.

Fluid Mechanics

Bernoulli, a Swiss physicist and mathematician, made important discoveries in fluid dynamics and published 'Hydrodynamica' in 1738. In this famous work, he incorporated theoretical and practical study of equilibrium, pressure, and speed in fluids.

Matter is found in three states viz., solid, liquid and gas.

Solid have definite shape and volume. They are not easily deformed by shearing force (tangential force applied along the surface) because cohesive forces between the molecules are very strong and hold molecules in a particular position and order.

Introduction to Fluid Mechanics

Liquids and gasesdo not have their own shape. A liquid can have a fixed volume but not a definite shape. It takes the shape of tehcontainer which holds it.

A gas has neither definite volume nor definite shape. A gas of given mass can fill the whole volume of its container, whether big or small. Liquids and gases can not sustain shearing force for the molecules in them are held together by  weak cohesive forces. An applied shearing force can cause a liquid or a gas to flow. A substance that can flow is called a fluid. So liquids and gases are known as fluids.

Fluid Mechanics

A fluid is a state of matter where in molecules are randomly arranged, cohesive forces between the molecules are weak, and offer negligible resistance to the shearing force. An ideal fluid offers no resistance to the shearing force at all.

Fluids can be compressible or incompressible. A compressible fluid is affected by a change in its volume upon the application of external force. An incompressible fluid has fixed volume and it is impossible to change its volume.

We breathe air and drink water. We use pneumatic and hydraulic machinery for various purposes in our daily life. These examples are enough for us to realize the importance of the study of fluids.

Fluid Mechanics : Introducing Bernoulli Theorem

The motion of objects in flowing fluid can be understood  by Bernoulli theorem.   It is stated like this :

" For a steady flow of a non-viscous, incompressible fluid sum of the pressure energy, kinetic energy and the potential energy per unit volume remains constant at all points. "

            The Equation is given by  :  P  +  img gh  +  (1)/(2)img v2  =  constant . 

 Here  v  =  flow speed

           P  = pressure

          img = density

         g = gravity

         h = height.

Introduction to fluid mechanics viscosity:

The internal resistance of the fluid that obstructs the flow of fluid is called viscosity. But all real fluids have some viscosity. To maintain the flow of a viscous fluid. We have to apply  an external force against the viscous forces. The pressure difference between two points of a tube is necessary to maintain the fluid flow.

Consider a liquid, flowing at a steady rate on a horizontal surface. The liquid can be assumed to be composed of different horizontal layers. The velocity of liquid at any point on any given horizontal layer is the same. But the velocity of liquid in the layers perpendicular to the direction of flow is different in different layers. The velocity of the upper layer of the liquid surface is maximum and that of the lower layer is lesser. Similarly the velocity goes on decreasing as the depth increases and finally the deepest layer in contact with the horizontal surface is at rest. So, there exists a velocity gradient perpendicular to the plane of the fluid. Let us see the definition for viscosity in fluid mechanics

Definition for Viscosity in Fluid Mechanics:

If a specific layer of a liquid is taken, the layer below it moving with lesser velocity, tries to decrease the velocity of upper layer due to cohesive forces between the molecules of adjacent layers. In turn the upper layer which is moving with greater velocity tries to increase the velocity of the lower layer. Thus between parallel, successive layers of a liquid in motion, opposing force comes into play tending to decrease the relative velocity between the layers. The force is called viscous drag. It looks like a tangential shearing force is acting between the layers. To overcome these  forces and for maintaining constant velocity between  layers, an external force need to be applied. If there is no external force, the velocity of flow decreases and becomes zero.

Conclusion on Viscosity in Fluid Mechanics

This property of a fluid which opposes the relative motion between different layers is called viscosity. This is the internal resistance of friction exhibited between the layers of a fluid. Liquids such as kerosene, alcohol, water etc., which flow easily are said to be mobile, while liquids like tar, glycerin honey etc which do not flow readily are said to be viscous.

Submit us an Assignment:

For Demo Class Click here
Read more